Functional self-similarity, scaling and a renormalization group calculation of the partition function for a non-ideal chain

The hypothesis of asymptotic self-similarity for nonideal polymer chains is used to derive the functional and differential equations of a new renormal ization group. These equations are used to calculate the partition function s of randomly jointed chains with hard-sphere excluded-volume interactions. Theoretical predictions are compared with Monte Carlo calculations based o n the same microscopic chain model. The excess partition function converges very slowly to its true asymptotic form deltaQ(N --> infinity) similar to kappa (N-1). The conventional asymptotic formula, deltaQ(N --> infinity) si milar to kappa N-N-1(gamma -1), is found to be applicable for chains of mod erate length and for excluded-volume interactions appropriate to the subcla ss of flexible self-avoiding chains. (C) 2001 Elsevier Science B.V. All rig hts reserved.